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We analyze convergence of the Levenberg-Marquardt method for solving nonlinear inverse problems in Hilbert spaces. Specifically, we establish local convergence and convergence rates for a class of inverse problems that satisfy H\"{o}lder…

Functional Analysis · Mathematics 2025-01-16 Akari Ishida , Sei Nagayasu , Gen Nakamura

We describe a numerical method for the solution of acoustic exterior scattering problems based on the time-domain boundary integral representation of the solution. As the spatial discretization of the resulting time-domain boundary integral…

Numerical Analysis · Mathematics 2022-03-03 Ebraheem Aldahham , Lehel Banjai

This paper is concerned with inverse scattering problems of determining the support of an isotropic and homogeneous penetrable body from knowledge of multi-static far-field patterns in acoustics and in linear elasticity. The normal…

Analysis of PDEs · Mathematics 2024-04-11 Chun Liu , Guanghui Hu , Jianli Xiang , Jiayi Zhang

In this paper we consider high-frequency acoustic transmission problems with jumping coefficients modelled by Helmholtz equations. The solution then is highly oscillatory and, in addition, may be localized in a very small vicinity of…

Numerical Analysis · Mathematics 2025-03-03 Silvia Falletta , Stefan Sauter

Scattering resonances arise in wave phenomena and play an important role in many applications. While extensive theoretical studies have been conducted, effective numerical computation remains limited, and most existing methods suffer from…

Numerical Analysis · Mathematics 2026-04-17 Bo Gong , Jiguang Sun

This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis of wave atoms, and compress by…

Numerical Analysis · Mathematics 2008-05-28 Laurent Demanet , Lexing Ying

In this short note, we present an easy to implement and fast algorithm for the computation of the steady solitary gravity wave solution of the free surface Euler equations in irrotational motion. First, the problem is reformulated in a…

Fluid Dynamics · Physics 2020-02-20 Didier Clamond , Denys Dutykh

We study the convergence of the Left-Right splitting method (equivalent in key respects to the Method of Multiple Ordered Interactions and Forward-Backward method) for wave scattering by rough surfaces. This is an operator series method…

Numerical Analysis · Mathematics 2025-08-19 Paul E Parbone , Mark Spivack , Orsola Rath Spivack

In this paper, we present the Stroboscopic Averaging Method (SAM), recently introduced in [7,8,10,12], which aims at numerically solving highly-oscillatory differential equations. More specifically, we first apply SAM to the Schr\"odinger…

Numerical Analysis · Mathematics 2013-08-07 Philippe Chartier , Norbert J. Mauser , Florian Méhats , Yong Zhang

This paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the…

Analysis of PDEs · Mathematics 2016-08-10 Gang Bao , Chuchu Chen , Peijun Li

A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…

Numerical Analysis · Mathematics 2016-05-23 Michael V. Klibanov , Hui Liu , Loc H. Nguyen

For the first time, we develop in this paper the globally convergent convexification numerical method for a Coefficient Inverse Problem for the 3D Helmholtz equation for the case when the backscattering data are generated by a point source…

Numerical Analysis · Mathematics 2020-02-14 Vo Anh Khoa , Michael Victor Klibanov , Loc Hoang Nguyen

Consider the inverse scattering of time-harmonic acoustic scattering by an infinite rough surface which is supposed to be a local perturbation of a plane. A novel version of reverse time migration (RTM) is proposed to reconstruct the shape…

Analysis of PDEs · Mathematics 2023-10-24 Jianliang Li , Hao Wu , Jiaqing Yang

This paper presents high-order integral equation methods for evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced…

Computational Physics · Physics 2015-06-19 Carlos Pérez-Arancibia , Oscar P. Bruno

A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…

Numerical Analysis · Mathematics 2020-07-31 Balázs Kovács , Buyang Li , Christian Lubich

In this paper, we propose a novel accelerated forward-backward splitting algorithm for minimizing convex composite functions, written as the sum of a smooth function and a (possibly) nonsmooth function. When the objective function is…

Optimization and Control · Mathematics 2025-09-19 Kansei Ushiyama

The semidiscretization of a sound soft scattering problem modelled by the wave equation is analyzed. The spatial treatment is done by integral equation methods. Two temporal discretizations based on Runge-Kutta convolution quadrature are…

Numerical Analysis · Mathematics 2024-07-25 Jens Markus Melenk , Alexander Rieder

We consider time domain acoustic scattering from a penetrable medium with a variable sound speed. This problem can be reduced to solving a time domain volume Lippmann-Schwinger integral equation. Using convolution quadrature in time and…

Numerical Analysis · Mathematics 2014-07-30 Armin Lechleiter , Peter Monk

We solve first-kind Fredholm boundary integral equations arising from Helmholtz and Laplace problems on bounded, smooth screens in three-dimensions with either Dirichlet or Neumann conditions. The proposed Galerkin-Bubnov method takes as…

Numerical Analysis · Mathematics 2020-11-12 Jose Pinto , Carlos Jerez-Hanckes

It is demonstrated that the Locally Corrected Nystrom (LCN) method is a versatile and numerically efficient computational method for the modeling of scattering from plasmonic bowtie nanoantennas. The LCN method is a high-order analysis…

Optics · Physics 2016-11-30 Hamid T. Chorsi , Stephen D. Gedney